Optical Member for Photolithography and Method of Evaluating the Same

ABSTRACT

A method of evaluating a refractive index homogeneity of an optical member for photolithography, the method comprising:  
     a measurement step of transmitting light having a predetermined wavelength λ through the optical member so as to measure a wavefront aberration;  
     a Zernike fitting step of expanding thus measured wavefront aberration into a polynomial of a Zernike cylindrical function system;  
     a first separating step of separating individual components of the polynomial into a rotationally symmetric element, an odd-symmetric element, and an even-symmetric element; and  
     a second separating step of separating individual components of the polynomial into a plurality of parts according to a degree thereof.

TECHNICAL FIELD

[0001] The present invention relates to an optical member forphotolithography, employed as an optical device such as a lens, prism,mirror, correction plate, or photomask for light in a specificwavelength region at 250 nm or shorter, preferably 200 nm or shorter, inthe UV lithography technology in particular; and a method of evaluatingthe same.

BACKGROUND ART

[0002] In photolithography exposure apparatus for making semiconductordevices such as LSI, liquid crystal display devices, thin-film magneticheads, or the like, a pattern on a projection original such as a mask orreticle is irradiated with light from a light source by way of anillumination optical system, and the pattern is projected by way of aprojection optical system onto a photosensitive substrate such as awafer or glass plate coated with photoresist beforehand, so as to carryout exposure. Types of the projection optical system include refractiontype projection optical systems constituted by lenses adapted totransmit/refract light at an exposure wavelength, reflection typeprojection optical systems constituted by mirrors adapted to reflectlight at the exposure wavelength, and catadioptric projection opticalsystems combining lenses and mirrors.

[0003] In recent years, as the degree of integration has been advancingin semiconductor devices and the like, patterns transferred onto asubstrate have been becoming finer. Therefore, photolithography exposureapparatus have been shifting their light sources from i-line (365 nm) toKrF excimer laser (248 nm) and ArF excimer laser (193 nm), and furtherto F₂ laser (157 nm), thus attaining shorter wavelengths. As aconsequence, higher optical performances have been required for opticalsystems for the photolithography exposure apparatus. In particular,projection optical systems for transferring fine mask patterns ontophotosensitive surfaces of wafers have been demanded to exhibit quitehigh optical performances with a high resolution and nearly zeroaberrations. For satisfying such a demand, a very high level has beenrequired for the refractive index homogeneity of optical members such aslenses, prisms, mirrors, and photomasks used as optical systems inphotolithography exposure apparatus (hereinafter referred to as opticalmembers for photolithography).

[0004] Meanwhile, it is important that optical members forphotolithography exhibit no unevenness in their refractive index (i.e.,have refractive index homogeneity). Conventionally, the refractive indexhomogeneity of an optical member for photolithography has been evaluatedby measuring the wavefront aberration occurring when light passesthrough the optical member, and using the difference between the maximumand minimum values (here in after referred to as PV value), root meansquare (hereinafter referred to as RMS value), or the like of thewavefront aberration as an evaluation index. Specifically, opticalmembers have been thought superior as their PV and RMS values aresmaller. Namely, in order to lower these values, optical membersconsidered to be of high quality have been made.

[0005] Japanese Patent Application Laid-Open No. HEI 8-5505 discloses aconventional refractive index homogeneity evaluating method. A specificprocedure of this method will be explained with reference to FIG. 1.

[0006] (1) An optical member for photolithography ground into a columnaror prismatic (rectangular parallelepiped) shape is set to aninterferometer, and a reference wavefront is perpendicularly emitted tothus ground surface, so as to measure wavefront aberration (S101).Information resulting from the refractive index distribution of theoptical member appears in thus measured wavefront aberration (S102,d101). In this information, an aberration error resulting from acurvature component is referred to as a power element or focus element,whereas that resulting from a tilt component is referred to as a tiltelement.

[0007] (2) The power and tilt elements are eliminated from the measuredwavefront aberration (S103, d102).

[0008] (3) Further, the wavefront aberration resulting from theastigmatic element is eliminated (S104, d103).

[0009] (4) The remaining wavefront aberrationis separated into arotationally symmetric element and a non-rotationally symmetric (random)element (S105).

[0010] (5) The PV and RMS values of the non-rotationally symmetric(random) element are determined, and evaluation is carried out accordingto these values (d104).

[0011] (6) By a least-squares method, the rotationally symmetric elementis fitted to an aspheric surface expression (S106), second- andfourth-order components are eliminated therefrom (S107), PV and RMSvalues of the remaining wavefront aberration components of sixth orhigher even order (hereinafter referred to as second- and fourth-orderresiduals) are determined, and evaluation is carried out according tothese values (d105).

[0012] As can be seen from the foregoing procedure, optical membershaving smaller non-rotationally symmetric (random) element and second-and fourth-order residuals have been considered optical members with afavorable refractive index homogeneity, and efforts have been made inorder to make such optical members. Namely, optical members have beenmade heretofore so as to suppress the non-rotationally symmetric elementand second- and fourth-order residuals to low levels.

[0013] However, optical systems constituted by optical members made soas to exhibit the same RMS and PV values of non-rotationally symmetricelement and second- and fourth-order residuals have often yieldedimaging performances different from each other. Also, there have beencases where a desirable imaging performance cannot be achieved even whenusing optical members which have been considered favorable according tothe evaluation based on the above-mentioned RMS and PV values. It isneedless to mention that semiconductor devices and the like with a highdegree of integration are hard to make when using such an optical systemfailing to achieve a desirable imaging performance. In particular,large-size photolithography optical members exceeding a diameter of 250mm and a thickness of 40 mm have been problematic in that thedisadvantages mentioned above occur frequently when evaluated by theconventional method.

DISCLOSURE OF THE INVENTION

[0014] The inventors have found that, by applying a fitting method basedon a Zernike cylindrical function system to the evaluation of refractiveindex homogeneity of individual optical members, the refractive indexhomogeneity of each optical member can be evaluated more accurately,whereby an optical system achieving a higher-level imaging performancecan be constructed more reliably as compared with the case using aconventional refractive index homogeneity evaluating method. Namely,according to the present invention, a photolithography optical memberhaving a high refractive index homogeneity and high quality can beprovided more reliably, and not only a high-precision photolithographyoptical system but also a high-performance photolithography exposureapparatus can be made reliably with a high efficiency.

[0015] The present invention provides a method of evaluating arefractive index homogeneity of an optical member for photolithography,the method comprising:

[0016] a measurement step of transmitting light having a predeterminedwavelength λ through the optical member so as to measure a wavefrontaberration;

[0017] a Zernike fitting step of expanding thus measured wavefrontaberration into a polynomial of a Zernike cylindrical function system;

[0018] a first separating step of separating individual components ofthe polynomial into a rotationally symmetric element, an odd-symmetricelement, and an even-symmetric element; and

[0019] a second separating step of separating individual components ofthe polynomial into a plurality of parts according to a degree thereof.

[0020] In the evaluating method of the present invention, the step(first separating step) of separating individual components of thepolynomial into the rotationally symmetric element, odd-symmetricelement, and even-symmetric element, and the step (second separatingstep) of separating individual components of the polynomial into aplurality of parts according to the degree thereof may be carried out inany order.

[0021] Preferably, in the second separating step, individual componentsof the polynomial are separated into three parts of lower, middle, andhigher orders according to the degree thereof. More preferably, thethree parts of lower, middle, and higher orders are terms where n=4 to8, n=9 to 35, and n>35 in the Zernike cylindrical function system,respectively, whereas a term where n=0 to 3 may be unused forevaluation.

[0022] Preferably, in the first and second separating steps is inaccordance with the present invention, individual components of thepolynomial are classified such that a rotationally symmetric element, anodd-symmetric element, and an even-symmetric element in a term where n=4to 8 become a lower-order rotationally symmetric element, a lower-orderodd-symmetric element, and a lower-order even-symmetric element,respectively; a rotationally symmetric element, an odd-symmetricelement, and an even-symmetric element in a term where n=9 to 35 becomea middle-order rotationally symmetric element, a middle-orderodd-symmetric element, and a middle-order even-symmetric element,respectively; and a rotationally symmetric element, an odd-symmetricelement, and an even-symmetric element in a term where n=36 to 80 becomea higher-order rotationally symmetric element, a higher-orderodd-symmetric element, and a higher-order even-symmetric element,respectively; and a term where n >80 becomes a residual in thepolynomial; and

[0023] the evaluating method in accordance with the present invention inthis case preferably further comprises:

[0024] an RMS value calculating step of calculating an RMS value of eachof the lower-order rotationally symmetric element, lower-orderodd-symmetric element, lower-order even-symmetric element, middle-orderrotationally symmetric element, middle-order odd-symmetric element,middle-order even-symmetric element, higher-order rotationallysymmetricelement, higher-order odd-symmetric element, higher-ordereven-symmetric element, and residual; and

[0025] an evaluating step of evaluating whether thus calculated RMSvalue satisfies a predetermined condition or not.

[0026] The evaluating step preferably evaluates whether at least one ofthe following conditions (a₁), (b₁), (c₁), and (d₁) is satisfied or not:

[0027] (a₁) each of the respective RMS values of the lower-orderrotationally symmetric element, lower-order odd-symmetric element, andlower-order even-symmetric element is 0.06λ or less;

[0028] (b₁) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.02λ or less;

[0029] (c₁) each of the respective RMS values of the higher-orderrotationally symmetric element, higher-order odd-symmetric element, andhigher-order even-symmetric element is 0.005λ or less; and

[0030] (d₁) the RMS value of the residual is 0.006λ or less; andparticularly preferably evaluates whether all of the above-mentionedconditions (a₁), (b₁), (c₁), and (d₁) are satisfied or not.

[0031] Further, the evaluating step preferably evaluates whether atleast one of the following conditions (a₂), (b₂), (c₂), and (d₂) issatisfied or not:

[0032] (a₂) each of the respective RMS values of the lower-orderrotationally symmetric element, lower-order odd-symmetric element, andlower-order even-symmetric element is 0.02λ or less;

[0033] (b₂) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.008λ or less;

[0034] (c₂) each of the respective RMS values of the higher-orderrotationally symmetric element, higher-order odd-symmetric element, andhigher-order even-symmetric element is 0.003λ or less; and

[0035] (d₂) the RMS value of the residual is 0.004λ or less; andparticularly preferably evaluates whether all of the above-mentionedconditions (a₂), (b₂), (c₂), and (d₂) are satisfied or not.

[0036] It is also preferred that, in the first and second separatingsteps in accordance with the present invention, individual components ofthe polynomial be classified such that a rotationally symmetric element,an odd-symmetric element, and an even-symmetric element in a term wheren =4 to 8 become a lower-order rotationally symmetric element, alower-order odd-symmetric element, and a lower-order even-symmetricelement, respectively; a rotationally symmetric element, anodd-symmetric element, and an even-symmetric element in a term where n=9to 35 become a middle-order rotationally symmetric element, amiddle-order odd-symmetric element, and a middle-order even-symmetricelement, respectively; and a term where n >35 becomes a higher-orderresidual in the polynomial; and

[0037] the evaluating method in accordance with the present invention inthis case preferably further comprises:

[0038] an RMS value calculating step of calculating an RMS value of eachof the lower-order rotationally symmetric element, lower-orderodd-symmetric element, lower-order even-symmetric element, middle-orderrotationally symmetric element, middle-order odd-symmetric element,middle-order even-symmetric element, and higher-order residual; and

[0039] an evaluating step of evaluating whether thus calculated RMSvalue satisfies a predetermined condition or not.

[0040] The evaluating step preferably evaluates whether at least one ofthe following conditions (a₃), (b₃), and (c₃) is satisfied or not:

[0041] (a₃) each of the respective RMS values of the lower-orderrotationally symmetric element, lower-order odd-symmetric element, andlower-order even-symmetric element is 0.06λ or less;

[0042] (b₃) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.02λ or less; and

[0043] (c₃) the RMS value of the higher-order residual is 0.01λ or less;and particularly preferably evaluates whether all of the above-mentionedconditions (a₃), (b₃), and (c₃) are satisfied or not.

[0044] Further, the evaluating step preferably evaluates whether atleast one of the following conditions (a₄), (b₄), and (c₄) is satisfiedor not:

[0045] (a₄) each of the respective RMS values of the lower-orderrotationally symmetric element, lower-order odd-symmetric element, andlower-order even-symmetric element is 0.02λ or less;

[0046] (b₄) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.008λ or less; and

[0047] (c₄) the RMS value of the higher-order residual is 0.004λ orless; and particularly preferably evaluates whether all of theabove-mentioned conditions (a₄), (b₄), and (c₄) are satisfied or not.

[0048] Also, the present invention provides an optical member forphotolithography used in a specific wavelength band at a wavelength of250 nm or shorter;

[0049] wherein, while a wavefront aberration measured upon transmittinglight having a wavelength λ through the optical member is expanded intoa polynomial of a Zernike cylindrical function system, a rotationallysymmetric element, an odd-symmetric element, and an even-symmetricelement in a term where n=4 to 8 are defined as a lower-orderrotationally symmetric element, a lower-order odd-symmetric element, anda lower-order even-symmetric element, respectively; a rotationallysymmetric element, an odd-symmetric element, and an even-symmetricelement in a term where n=9 to 35 are defined as a middle-orderrotationally symmetric element, a middle-order odd-symmetric element,and a middle-order even-symmetric element, respectively; and arotationally symmetric element, an odd-symmetric element, and aneven-symmetric element in a term where n=35 to 80 are defined as ahigher-order rotationally symmetric element, a higher-orderodd-symmetric element, and a higher-order even-symmetric element,respectively; and a term where n >80 is defined as a residual; theoptical member satisfying at least one of the following conditions (a₁),(b₁), (c₁) and (d₁):

[0050] (a₁) each of the respective RMS values of the lower-orderrotationally symmetric element, lower-order odd-symmetric element, andlower-order even-symmetric element is 0.06λ or less;

[0051] (b₁) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.02λ or less;

[0052] (c₁) each of the respective RMS values of the higher-orderrotationally symmetric element, higher-order odd-symmetric element, andhigher-order even-symmetric element is 0.005λ or less; and

[0053] (d₁) the RMS value of the residual is 0.006λ or less; and it isparticularly preferable that the optical member satisfy all of theabove-mentioned conditions (a₁), (b₁) (c₁), and (d₁).

[0054] Also, the optical member preferably satisfies at least one of thefollowing conditions (a₂), (b₂), (c₂), and (d₂):

[0055] (a₂) each of the respective RMS values of the lower-orderrotationally symmetric element, lower-order odd-symmetric element, andlower-order even-symmetric element is 0.02λ or less;

[0056] (b₂) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.008λ or less;

[0057] (c₂) each of the respective RMS values of the higher-orderrotationally symmetric element, higher-order odd-symmetric element, andhigher-order even-symmetric element is 0.003λ or less; and (d₂) the RMSvalue of the residual is 0.004λ or less; and particularly preferablysatisfies all of the above-mentioned conditions (a₂), (b₂), (c₂), and(d₂).

[0058] Further, the present invention provides an optical member forphotolithography used in a specific wavelength band at a wavelength of250 nm or shorter;

[0059] wherein, while a wavefront aberration measured upon transmittinglight having a wavelength λ through the optical member is expanded intoa polynomial of a Zernike cylindrical function system, a rotationallysymmetric element, an odd-symmetric element, and an even-symmetricelement in a term where n=4 to 8 are defined as a lower-orderrotationally symmetric element, a lower-order odd-symmetric element, anda lower-order even-symmetric element, respectively; a rotationallysymmetric element, an odd-symmetric element, and an even-symmetricelement in a term where n=9 to 35 are defined as a middle-orderrotationally symmetric element, a middle-order odd-symmetric element,and a middle-order even-symmetric element, respectively; and a termwhere n >35 is defined as a higher-order residual; the optical membersatisfying at least one of the following conditions (a₃) (b₃), and (c₃):

[0060] (a₃) each of the respective RMS values of the lower-orderrotationally symmetric element, lower-order odd-symmetric element, andlower-order even-symmetric element is 0.06λ or less;

[0061] (b₃) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.02λ or less; and

[0062] (c₃) the RMS value of the higher-order residual is 0.01λ or less;and particularly preferably satisfying all of the above-mentionedconditions (a₃), (b₃), and (c₃).

[0063] Also, the optical member preferably satisfies at least one of thefollowing conditions (a₄), (b₄), and (c₄):

[0064] (a₄) each of the respective RMS values of the lower-orderrotationally symmetric element, lower-order odd-symmetric element, andlower-order even-symmetric element is 0.02λ or less;

[0065] (b₄) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.008λ or less; and

[0066] (c₄) the RMS value of the higher-order residual is 0.004λ orless; and particularly preferably satisfies all of the above-mentionedconditions (a₄), (b₄), and (c₄).

[0067] Also, the present invention provides a projection optical systememployed in a photolithography exposure apparatus used in a specificwavelength band at a wavelength of 250 nm or shorter, wherein at least90% of lenses constituting the projection optical system comprise theoptical member in accordance with the present invention.

[0068] In the projection optical system of the present invention, it isparticularly preferred that, in the above-mentioned lenses, a lenshaving a luminous flux diameter/effective diameter of ½ or less comprisean optical member satisfying all of the above-mentioned conditions (a₂),(b₂), (c₂), and (d₂) or an optical member satisfying all of theabove-mentioned conditions (a₄), (b₄), and (c₄).

[0069] Further, the present invention provides a photolithographyexposure apparatus used in a specific wavelength band at a wavelength of250 nm or shorter, the exposure apparatus comprising the projectionoptical system of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0070]FIG. 1 is a flowchart showing a method of evaluating therefractive index homogeneity of a photolithography optical member whichhas conventionally been carried out;

[0071]FIG. 2 is a flowchart showing a preferred embodiment of the methodof evaluating the refractive index homogeneity of a photolithographyoptical member in accordance with the present invention;

[0072]FIG. 3 is a flowchart showing another preferred embodiment of themethod of evaluating the refractive index homogeneity of aphotolithography optical member in accordance with the presentinvention;

[0073]FIGS. 4A and 4B are schematic side views showing respective statesin which an optical member is measured in terms of wavefront;

[0074]FIG. 5 is a schematic sectional view showing an embodiment of aprojection optical system for an excimer laser stepper;

[0075]FIG. 6 is a schematic plan view for explaining a coordinate systemrepresenting measured wavefront aberration data;

[0076]FIG. 7A is a schematic side view showing a state in which anoptical member is measured in terms of wavefront while being rotated,whereas FIG. 7B is a schematic plan view showing the optical member asseen in the direction of line b-b in FIG. 7A;

[0077]FIG. 8A is a schematic side view showing a state in which anoptical member is measured in terms of wavefront while being shiftedsidewise, whereas FIG. 8B is a schematic plan view showing the opticalmember as seen in the direction of line b-b in FIG. 8A;

[0078]FIG. 9 is a schematic exploded view for explaining steps ofobtaining an optical member from an ingot;

[0079]FIG. 10 is a schematic side view showing an embodiment of excimerlaser stepper; and

[0080]FIG. 11 is a schematic side view showing the principle ofevaluating wavefront aberration, which is effected by a Fizeau typeinterferometer for measuring optical systems.

BEST MODES FOR CARRYING OUT THE INVENTION

[0081] In the following, preferred embodiments of the present inventionwill be explained in detail with reference to the drawings whenappropriate. In the drawings, parts identical or equivalent to eachother will be referred to with numerals identical to each other.

[0082] First, materials are combined together, so as to synthesize aningot. Employed as the materials are synthetic silica glass,fluorine-doped silica glass, calcium fluoride, barium fluoride, othercrystal materials, and the like. Since synthesizing methods varydepending on the kinds of materials, they are synthesized by methodssuitable for the individual materials. A photolithography optical memberis cut out from thus synthesized ingot. The optical member has adiameter of 300 mm and a thickness of 60 mm, for example, whereas itsupper and lower faces are subjected to high-precision polishing orgrinding.

[0083] The wavefront aberration of the optical member is measured, forexample, by a Fizeau type interferometer, using an He-Ne laser at awavelength of 633 nm as a light source, for measuring flat opticalmembers. This interferometer has a structure capable of fixing an objectto be measured between two plane-parallel plate members. Though lightsources employed for wavefront aberration measurement more fundamentallyuse KrF excimer lasers (248 nm) or ArF excimer lasers (193 nm), theHe-Ne lasers are often used due to such reasons as the cost, size, andmeasurement stability of the interferometer.

[0084] The measurement of wavefront aberration is carried out by anoil-on-platemethod. This method will be explained specifically withreference to the flowcharts of FIGS. 2 and 3, and explanatory views ofFIGS. 4A and 4B.

[0085] First, an interferometer is prepared. As shown in FIGS. 4A and4B, the interferometer comprises a body part 41, a reference surfaceobject 42, two plane-parallel plate members 43, and a reflecting surface45. Before setting an optical member 44, which is an object to bemeasured, to this interferometer, the gap between the two plane-parallelplate members 43 is filled with a transparent oil 46 having a refractiveindex identical to that of the object to be measured and is irradiatedin this state with a reference wavefront formed by a laser beam, whereasthe light transmitted therethrough is captured, so as to obtainwavefront data (S201, S301). This state is shown in FIG. 4A.Subsequently, in the state where the optical member 44 is set betweenthe two plane-parallel plate members 43, the gaps between theplane-parallel plate members 43 and the optical member 44 are filledwith the transparent oil 46, and the light transmitted therethrough iscaptured in this state, so as to obtain wavefront data. This state isshown in FIG. 4B.

[0086] Then, the wavefront data measured in the state setting no opticalmember is subtracted from the wavefront data measured in the statesetting the optical member 44. This eliminates not only the influence ofmeasurement errors due to the wavefront aberration caused by the surfaceform of the optical member 44, but also errors due to the wavefrontaberration caused by the interferometer, whereby the wavefrontaberration within the optical member 44 can be measured alone. Namely,the wavefront aberration inherent in the optical member can bedetermined (S202, S302).

[0087] Preferably, in the case where the cross section is circular, asquare area circumscribing this circle is divided into about 50×50 meshor more, and the measurement value of each of thus divided elements isobtained. The number of elements (number of measurement points) ispreferably changed according to the diameter of the object to bemeasured, and is more preferably determined according to the luminousflux diameter (partial diameter). For example, while the luminous fluxtransmitted through a reticle R in the optical system (projectionoptical system) shown in FIG. 5 passes through lens groups G1 to G6, soas to be focused on a surface of a wafer W, the respective luminous fluxdiameters (partial diameters) transmitted through the individual lensesvary. Namely, the luminous flux diameter in lenses closer to the reticleR is smaller than that in lenses farther from the reticle R (closer tothe wafer W). Respective optical members for processing individuallenses can be measured at substantially the same accuracy when thenumber of measurement points is selected so as to become substantiallyidentical within the luminous flux diameters of the lenses. Here, thenumber of measurement points becomes very large when measuring the wholeeffective lens diameter of an optical member used for a lens having asmall luminous flux with respect to the effective diameter. In thiscase, the wavefront a berration measurement may be carried out for eachof a plurality of regions in the optical member, and thus obtainedwavefront aberration data may be combined together, whereby thewavefront aberration of the whole optical member can be obtained.

[0088] For the wavefront aberration measurement, Twyman-Green typeinterferometers, shearing type interferometers, and the like may be usedas well.

[0089] As shown in FIG. 6, a coordinate system is defined on the exitpupil surface of the optical member, so as to represent the measuredwavefront aberration. Namely, polar coordinates are defined on the exitpupil surface, and the wavefront aberration W is represented as

W(ρ,θ).

[0090] Further, it is expanded into an orthogonal function system. Inthe present invention, for separating the wavefront aberration into arotationally symmetric element, an odd-symmetric element, and aneven-symmetric element about the pupil of the optical member, polarcoordinates are used as a coordinate system, and a Zernike cylindricalfunction is used as an orthogonal function system. Here, ρ is thenormalized pupil radius taking the radius of exit pupil as 1, and θ isthe directional angle of radius vector in polar coordinates. Namely,using a Zernike cylindrical function system Zn (ρ,θ), wavefrontaberration W (ρ,θ) is expanded as

W(ρ,θ)=ΣCnZn(ρ,θ)  (1)

[0091] (S203, S303). Here, Cn is the expansion coefficient. Fitting canbe effected with a higher accuracy as the expansion reaches a greater nvalue. However, it is desirable for n to be of an appropriate dimensionsince the burden on calculation will be heavier if n is too large. Fromsuch a viewpoint, it will be suitable if n=0 to 35 or n=0 to 80. Fittingup to the 10th-order coefficient is possible when n=0 to 35, whereasfitting up to the 16th-order coefficient is possible when n=0 to 80.

[0092] For example, a Zernike cylindrical function system Zn(ρ,θ) in thecase where n=0 to 35 is as follows:

[0093] n: Zn(ρ,θ)

[0094] 0: 1

[0095] 1: ρcosθ

[0096] 2: ρsinθ

[0097] 3: 2ρ²−1

[0098] 4: ρ²cos2θ

[0099] 5: ρ²sin2θ

[0100] 6: (3ρ²−2)ρcosθ

[0101] 7: (3ρ²−2)ρsinθ

[0102] 8: 6ρ⁴−6ρ²+1

[0103] 9: ρ³cos3θ

[0104] 10: ρ³sin3θ

[0105] 11: (4ρ²−3)ρ²cos2θ

[0106] 12: (4ρ²−3)ρ²sin2θ

[0107] 13: (10 ρ⁴−12ρ²+3)ρcosθ

[0108] 14: (10 ρ⁴−12ρ²+3)ρsinθ

[0109] 15: 20ρ⁶−30ρ⁴+12ρ²−1

[0110] 16: ρ⁴cos4θ

[0111] 17: ρ⁴ sin 4 θ

[0112] 18: (5ρ²−4)ρ³cos3θ

[0113] 19: (5ρ²−4)ρ³sin3θ

[0114] 20: (15ρ⁴−20ρ²+6)ρ²cos2θ

[0115] 21: (15ρ⁴−20ρ²+6)ρ²sin2θ

[0116] 22: (35ρ⁶−60ρ⁴+ρ²−4)ρcosθ

[0117] 23: (35ρ⁶−60ρ⁴+ρ²−4)ρsinθ

[0118] 24: 70ρ⁸−140ρ⁶+90ρ⁴−20ρ²+1

[0119] 25: ρ⁵ cos5θ

[0120] 26: ρ⁵ sin5θ

[0121] 27: (6ρ²−5)ρ⁴cos4θ

[0122] 28: (6ρ²−5)ρ⁴sin4θ

[0123] 29: (21ρ⁴−30ρ²+10)ρ³cos3θ

[0124] 30: (21ρ⁴−30ρ²+10)ρ³sin3θ

[0125] 31: (56ρ⁶−104ρ⁴+60ρ²−10)ρ²cos2θ

[0126] 32: (56ρ⁶−104ρ⁴+60ρ²−10)ρ²sin2θ

[0127] 33: (126ρ⁸−280ρ⁶+210ρ⁴−60ρ²+5)ρcosθ

[0128] 34: (126ρ⁸−280ρ⁶+210ρ⁴−60ρ²+5)ρsinθ

[0129] 35: 252ρ¹⁰−630ρ⁸+560ρ⁶−210ρ⁴+30ρ²−1

[0130] Zernike cylindrical function systems Zn(ρ,θ) in the case wheren=36 and greater will not be explained here.

[0131] Subsequently, the individual terms of expression (1) areseparated into the following three kinds (S204, S304):

[0132] (a) terms not including θ, i.e., a rotationally symmetric elementin which a value on a certain set of coordinates and a value on a set ofcoordinates obtained when the former coordinates are rotated by a givenangle about the center of pupil equal each other;

[0133] (b) terms including trigonometric functions of odd multiples ofthe directional angle of radius vector θ such as sin(or cos)θ and sin(orcos)3θ, i.e., an odd-symmetric element in which a value on a certain setof coordinates and a value on a set of coordinates obtained when theformer coordinates are rotated by odd submultiples of 360° about thecenter of pupil equal each other; and

[0134] (c) terms including trigonometric functions of even multiples ofthe directional angle of radius vector θ such as sin(or cos)2θ and sin(or cos)4θ, i.e., an even-symmetric element in which a value on acertain set of coordinates and a value on a set of coordinates obtainedwhen the former coordinates are rotated by even submultiples of 360°about the center of pupil equal each other. Namely, letting W_(rot),W_(odd), and W_(evn) be the rotationally symmetric element,odd-symmetric element, and even-symmetric element of wavefrontaberration,

W _(rot)(ρ,θ)=C ₀ +C ₃ Z ₃ +C ₈ Z ₈ +C ₁₅ Z ₁₅ +C ₂₄ Z ₂₄+  (2),

W _(odd)(ρ,θ)=C ₁ Z ₁ +C ₂ Z ₂ +C ₆ Z ₆ C ₇ Z ₇ +C ₉ Z ₉ +C ₁₀ Z ₁₀  (3),

[0135] and

W _(evn)(ρ,θ)=C ₄ Z ₄ +C ₅ Z ₅ +C ₁₁ Z ₁₁ +C ₁₂ Z ₁₂ +C ₁₆ Z ₁₆+  (4),

[0136] Further, let r_(w) be the RMS value (root mean square) of thewavefront aberration in expression (1), r_(rot) be the RMS value of therotationally symmetric element W_(rot) of wavefront aberration inexpression (2), r_(odd) be the RMS value of the odd-symmetric elementW_(odd) of wavefront aberration in expression (3), and r_(evn) be theRMS value of the even-symmetric element W_(evn) of wavefront aberrationin expression (4). Among r_(w), r_(rot), r_(odd), and r_(evn), therelationship of (r_(w))²=(r_(rot))²+(r_(odd))² +(r_(evn))² holds.

[0137] r_(cot), r_(odd), and r_(evn) can be related to the sphericalaberration element, coma aberration element, and astigmatism aberrationelement in the refractive index distribution of the optical member,respectively.

[0138] A case where optical members are processed into lenses, which arethen combined together to construct an optical system will be consideredhere. The aberration of elements having a relatively small n value,i.e., elements having a relatively low degree, is easy to decrease bychanging the lens gaps, rotating some of the lenses about the opticalaxis, tilting them, or shifting them. Aberration elements having agreater degree of n are harder to decrease, but can be reduced to someextent by rotating the lenses or changing the combination of lenses.When not reduced by such a method, aberration elements can be reduced bymodifying surface forms of some lenses. However, aberration elementshaving a further greater degree of n are hard to decrease.

[0139] According to the inventors' studies, the aberration can beeliminated in elements having a smaller n value, e.g., elements in whichn=0 to 3, so that there are no problems even when these elements areexcluded from objects to be evaluated. When elements whose n is 4 orgreater are divided into a plurality of regions according to thedimension of n and their aberration elements are evaluated, therefractive index homogeneity of the optical member can be evaluatedreasonably. For example, when the components are divided into threeregions such that elements whose n=4 to 8 are defined as a lower order,elements whose n=9 to 35 are defined as a middle order, and elementswhose n>35 are defined as a higher order, and then evaluation ofaberration elements is carried out, the refractive index homogeneity ofthe optical member can be evaluated reasonably (S205, S305).

[0140] Then, when each of W_(rot), W_(odd), and W_(evn) is divided intoa lower order (n=4 to 8), a middle order (n=9 to 35), and a higher order(n>35), they can be written from expressions (2), (3), and (4) asfollows:

lower-order W _(rot)(ρ,θ)=C ₈ Z ₈  (5)

lower-order W _(odd)(ρ,θ)=C ₆ Z ₆ +C ₇ Z ₇  (6)

lower-order W _(evn)(ρ,θ)=C ₄ Z ₄ +C ₅ Z ₅  (7)

middle-order W _(rot)(ρ,θ)=C ₁₅ Z ₁₅ +C ₂₄ Z ₂₄ +C ₃₅ Z ₃₅  (8)

middle-order W _(odd)(ρ,θ)=C ₉ Z ₉ +C ₁₀ Z ₁₀ +C ₁₃ Z ₁₃ +C ₁₄ Z ₁₄ +C₁₈ Z ₁₈ +C ₁₉ Z ₁₉ +C ₂₂ Z ₂₂ +C ₂₃ Z ₂₃ +C ₂₅ Z ₂₅ +C ₂₆ Z ₂₆ +C ₂₉ Z₂₉ +C ₃₀ Z ₃₀ +C ₃₃ Z ₃₃ +C ₃₄ Z ₃₄  (9)

middle-order W _(evn)(ρ,θ)=C ₁₁ Z ₁₁ +C ₁₂ Z ₁₂ +C ₁₆ Z ₁₆ +C ₁₇ Z_(17 +C) ₂₀ Z ₂₀

+C_(2l) Z ₂₁ +C ₂₇ Z ₂₇ +C ₂₈ Z ₂₈ +C ₃₁ Z ₃₁ +C ₃₂ Z ₃₂  (10)

higher-order W _(rot)(ρ,θ)=C ₃₅ Z ₃₅ +C ₄₈ Z ₄₈ +C ₆₃ Z ₆₃ +C ₈₀ Z₈₀  (11)

higher-order W _(odd)(ρ,θ)=C ₃₈ Z ₃₈ +C ₃₉ Z ₃₉ +C ₄₂ Z ₄₂ +C ₄₃ Z ₄₃ +C₄₆ Z ₄₆ +C ₄₇ Z ₄₇ +C ₄₉ Z ₄₉ +C ₅₀ Z ₅₀ +C ₅₃ Z ₅₃ +C ₅₄ Z ₅₄ +C ₅₇ Z₅₇ +C ₆₁ Z ₆₁ +C ₆₂ Z ₆₂ +C ₆₆ Z ₆₆ +C ₆₇ Z ₆₇ +C ₇₀ Z ₇₀ +C ₇₁ Z ₇₁ +C₇₄ Z ₇₄ +C ₇₅ Z ₇₅ +C ₇₈ Z ₇₈ +C ₇₉Z₇₉  (12)

higher-order W _(evn)(ρ,θ)=C ₃₆ Z ₃₆ +C ₃₇ Z ₃₇ +C ₄₀ Z ₄₀ +C ₄₁ Z ₄₁ +C₄₄ Z ₄₆ +C ₄₅ Z ₄₅ +C ₅₁ Z ₅₁ +C ₅₂ Z ₅₂ +C ₅₅ Z ₅₅ +C ₅₆ Z ₅₆ +C ₅₉ Z₅₉ C ₆₀ Z ₆₀ +C ₆₄ Z ₆₄ +C ₆₅ Z ₆₅ +C ₆₈ Z ₆₈ +C ₆₉ Z ₆₉ +C ₇₂ Z ₇₂ +C₇₃ Z ₇₃ +C ₇₃ +C ₇₆ Z ₇₆ ⇄C ₇₇ Z ₇₇  (13)

[0141] Then, the respective RMS values of these wavefront aberrationelements are defined as lower-order r_(rot), lower-order r_(odd),lower-order r_(evn), middle-order r_(rot), middle-order r_(odd),middle-order r_(evn), higher-order r_(rot), higher-order r_(odd), andhigher-order r_(evn), whereas the wavefront aberration element leftunfitted is defined as a residual. Also, the RMS and PV values of theresidual are defined as the residual RMS and residual PV, respectively(S206->d201).

[0142] When fitted while n=0 to 35, the higher-order r_(rot),higher-order r_(odd), and higher-order r_(evn), are not defined, whereasthe wavefront aberration element left unfitted in the lower- andmiddle-order terms is defined as a higher-order residual. Then, the RMSand PV values of the higher-order residual are defined as higher-orderresidual RMS and higher-order residual PV, respectively (S306->d301).

[0143] Though the wavefront aberration is initially separated into arotationally symmetric element, an odd rotationally symmetric element,and an even rotationally symmetric element, and then each element isseparated into lower, middle, and higher orders according to the degreethereof here, this order maybe reversed as a matter of course. Namely,totally the same results are obtained when the wavefront aberration isinitially separated into lower-, middle-, and higher-order elementsaccording to the degree thereof and then each element is separated intoa rotationally symmetric element, an odd rotationally symmetric element,and an even rotationally symmetric element.

[0144] The inventors made optical members having various characteristicsin terms of the refractive index homogeneity, classified them accordingto their refractive index homogeneity levels, constructedphotolithography projection optical systems by combining the opticalmembers at their respective levels, and evaluated their opticalperformances.

[0145] As a result, it has been found that, letting λ be the wavelengthof the light source, optical members whose lower-order r_(rot) is 0.06λor less, lower-order r_(odd) is 0.06λ or less, and lower-order r_(evn)is 0.06λ or less, or middle-order r_(rot) is 0.02λ or less, middle-orderr_(odd) is 0.02λ or less, and middle-order r_(evn) is 0.02λ or less, orhigher-order r_(rot) is 0.005λ or less, higher-order r_(odd) is 0.005λor less, and higher-order r_(evn) is 0.005λ or less, or residual RMS is0.006λ or less can yield favorable optical performances forphotolithography.

[0146] It has also been found that optical members whose lower-orderr_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ or less, andlower-order r_(evn) is 0.02λ or less, or middle-order r_(rot) is 0.008λor less, middle-order r_(odd) is 0.008λ or less, and middle-orderr_(evn) is 0.008λ or less, or higher-order r_(rot) is 0.003λ or less,higher-order r_(odd) is 0.003λ or less, and higher-order r_(evn) is0.003λ or less, or residual RMS is 0.004λ or less can yield morefavorable optical performances for photolithography and are particularlypreferable as optical members for projection optical systems.

[0147] It has also been found that optical members whose lower-orderr_(rot) is 0.06λ or less, lower-order r_(odd) is 0.06λ or less, andlower-order r_(evn) is 0.06λ or less, and middle-order r_(rot) is 0.02λor less, middle-order r_(odd) is 0.02λ or less, and middle-order r_(evn)is 0.02λ or less, and higher-order r_(rot) is 0.005λ or less,higher-order r_(odd) is 0.005λ or less, and higher-order r_(evn) is0.005λ or less, and residual RMS is 0.006λ or less can yield furtherfavorable optical performances for photolithography.

[0148] It has also been found that optical members whose lower-orderr_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ or less, andlower-order r_(evn) is 0.02λ or less, and middle-order r_(rot) is 0.008λor less, middle-order r_(odd) is 0.008λ or less, and middle-orderr_(evn) is 0.008λ or less, and higher-order r_(rot) is 0.003λ or less,higher-order r_(odd) is 0.003λ or less, and higher-order r_(evn) is0.003λ or less, and residual RMS is 0.004λ or less can yield furtherfavorable optical performances for photolithography and are particularlypreferable as optical members for projection optical systems.

[0149] It has also been found that, when fitted while n=0 to 35, opticalmembers whose lower-order r_(rot) is 0.06λ or less, lower-order r_(odd)is 0.06λ or less, and lower-order r_(evn) is 0.06λ or less, ormiddle-order r_(rot) is 0.02λ or less, middle-order r_(odd) is 0.02λ orless, and middle-order r_(evn) is 0.02λ or less, or higher-orderresidual RMS is 0.01λ or less can yield favorable optical performancesfor photolithography and are usable as optical members for projectionoptical systems.

[0150] It has also been found that optical members whose lower-orderr_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ or less, andlower-order r_(evn) is 0.02λ or less, or middle-order r_(rot) is 0.008λor less, middle-order r_(odd) is 0.008λ or less, and middle-orderr_(evn) is 0.008λ or less, or higher-order residual RMS is 0.004λ orless can yield favorable optical performances for photolithography andare particularly preferable as optical members for projection opticalsystems.

[0151] It has also been found that optical members whose lower-orderr_(rot) is 0.06λ or less, lower-order r_(odd) is 0.06λ or less, andlower-order r_(evn) is 0.06λ or less, and middle-order r_(rot) is 0.02λor less, middle-order r_(odd) is 0.02λ or less, and middle-order r_(evn)is 0.02λ or less, and higher-order residual RMS is 0.01λ or less canyield more favorable optical performances for photolithography.

[0152] It has also been found that optical members whose lower-orderr_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ or less, andlower-order r_(evn) is 0.02λ or less, and middle-order r_(rot) is 0.008λor less, middle-order r_(odd) is 0.008λ or less, and middle-orderr_(evn) is 0.008λ or less, and higher-order residual RMS is 0. 004λ orless can yield further favorable optical performances forphotolithography and are particularly preferable as optical members forprojection optical systems.

[0153] Here, a projection optical system employed in a photolithographyexposure apparatus will be explained with reference to FIG. 5. Aluminous flux transmitted through a reticle R passes through a pluralityof lens groups G1 to G6, so as to be focused onto a surface of a waferW. While the unevenness in refractive index of each lens adverselyaffects the imaging performance on the wafer surface, its magnitudevaries depending on the degree of elements. Namely, the lower-, middle-,and higher-order elements tend to increase their influence on theimaging performance successively in this order. The reason therefor willbe explained in the following. First, means for correcting wavefrontcomponents as an optical system include adjustment of lens gaps,rotating/shifting/tilting of lenses, and the like for the lower-orderelement; moderate aspheric surface processing of lens surfaces,compressing of lenses from two directions, application of pressurebetween lenses, and the like for the middle-order element; andcomplicated aspheric surface processing of lens surfaces, compressing oflenses from a multitude of directions, and the like for the higher-orderelement. Means for processing lens surfaces into complicated asphericsurfaces include, for example, fine processing of lens surfaces bygrinding with small-size grinding tools or magnetic fluids, ion beamirradiation, CVM (Chemical Vapor Milling), and the like. These meansbecome successively harder to attain for lower, middle, and higherorders. This is the reason why the lower-, middle-, and higher-orderelements successively increase their influence on imaging performancesin this order.

[0154] Namely, the importance of evaluation is the highest in thehigher-order element, and successively decreases in the middle- andlower-order elements. Therefore, while it is the most desirable that allof the lower-, middle-, and higher-order elements be evaluated, theaimed object will be achieved to a certain extent if only thehigher-order element or only the higher- and middle-order elements areevaluated.

[0155] On the other hand, the influence of the higher-order element onthe imaging performance is not the same among the lenses. When theluminous flux diameter (partial diameter) is taken into consideration inFIG. 5, it can be seen that the luminous flux diameter of a lens closerto the reticle R is smaller than that of a lens farther from the reticleR (closer to the wafer W). Therefore, the magnitude of adverse affect ofthe unevenness in refractive index with in a lens upon the imagingperformance on the wafer is much greater in a lens closer to the reticlethan in a lens farther from the reticle. In particular, this influenceis greater in lenses whose value of luminous flux diameter/effectivediameter is less than ½. Therefore, lenses having a luminous fluxdiameter/effective diameter value smaller than ½ (located closer to thereticle R) can yield a further favorable imaging performance if anoptical member having a smaller higher-order element RMS is usedtherefor.

[0156] Hence, it is preferred that at least 90% of the lensesconstituting the projection optical system comprise the optical memberof the present invention, and it is more preferable that all the lensescomprise the optical member of the present invention.

[0157] Preferably at least 90% of the lenses having a luminous fluxdiameter/effective diameter of ½ or less in the lenses constituting theprojection optical system comprise an optical member whose lower-orderr_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ or less, andlower-order r_(evn) is 0.02λ or less, and middle-order r_(rot) is 0.008λor less, middle-order r_(odd) is 0.008λ or less, and middle-orderr_(evn) is 0.008λ or less, and higher-order r_(rot) is 0.003λ or less,higher-order r_(odd) is 0.003λ or less, and higher-order r_(evn) is0.003 or less, and residual RMS is 0.004λ or less; and more preferablyall the lenses comprise an optical member satisfying the conditionmentioned above. Preferably at least 90% of the lenses having a luminousflux diameter/effective diameter of ½ or less in the lenses constitutingthe projection optical system comprise an optical member whoselower-order r_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ orless, and lower-order r_(evn) is 0.02λ or less, and middle-order r_(rot)is 0.008λ or less, middle-order r_(odd) is 0.008λ or less, andmiddle-order r_(evn) is 0.008λ or less, and higher-order residual RMS is0.004λ or less; and particularly preferably all the lenses comprise anoptical member satisfying the condition mentioned above.

[0158] As explained above, the oil-on-plate method is a measurementmethod in which the wavefront aberration measured in a state withoutsetting an object to be measured is subtracted from the wavefrontaberration measured in a state setting the object, so as to eliminatenot only the influence of wavefront aberration caused by the wavefrontaberration due to the surface form of the object but also the part ofwavefront aberration caused by the interferometer, whereby the wavefrontaberration within the object can be measured alone. Namely, letting W bethe wavefront aberration depending on the inner homogeneity of anoptical member as the object to be measured, E be the wavefrontaberration depending on the interferometer, and O be the wavefrontaberration depending on oil, the wavefront measurement data D₁ measuredin the state setting the optical member can be represented as

D ₁ =W+E+O.

[0159] Since the wavefront measurement data D₂ measured in the statewithout setting the optical member includes the wavefront aberration Edepending on the interferometer and the wavefront aberration O dependingon oil, it can be represented as

D ₂ =E+O.

[0160] Therefore, when the wavefront data D₂ measured in the statewithout setting the optical member is subtracted from the wavefront dataD₁ measured in the state setting the optical member,

D ₁ −D ₂ =W+E+O−(E+O)=W

[0161] whereby the wavefront aberration W depending on the innerhomogeneity can be isolated and determined alone.

[0162] However, it takes time for operations of setting an opticalmember to an interferometer and removing the former from the latter,whereby the state of the interferometer or oil may change due totemperature fluctuations and the like during this time. In actualmeasurement operations, in general, wavefront data is initiallydetermined before setting the optical member, and thus obtained data isused for measuring the wavefront aberration of a plurality of opticalmembers. In such a case, the initial data is used for a long period oftime, so that a greater temperature fluctuation may occur, therebycausing a possibility of greatly changing the states of interferometerand oil. Namely, E and O cannot be considered constant anymore, so thatthe wavefront aberration W inherent in the optical member cannot beisolated alone.

[0163] Therefore, in order to measure the wavefront aberration of theobject to be measured with a higher accuracy, the inventors propose thefollowing method. Namely, at first, an optical member as the object tobe measured is set to an interferometer, and wavefront data isdetermined. Subsequently, while rotating the optical member about theoptical axis, wavefront data is determined at each appropriate angle(FIGS. 7A and 7B).

[0164] Then, data obtained by averaging a plurality of wavefrontmeasurement data items at the respective angles is subtracted from thewavefront data measured before rotating the optical member. Thisdetermines the non-rotationally symmetric element in the rotationallysymmetric and non-rotationally symmetric elements constituting thewavefront aberration inherent in the opticalmember. Subsequently,wavefront data is determined in a state where the optical member isshifted in a direction perpendicular to the optical axis (FIGS. 8A and8B) and is subtracted from the wavefront data measured before shifting.

[0165] This determines the rotationally symmetric element in therotationally symmetric and non-rotationally symmetric elementsconstituting the wavefront aberration inherent in the optical member.Thus determined rotationally symmetric and non-rotationally symmetricelements are added together, whereby the wavefront aberration inherentin the optical member is determined. The time required for rotating orshifting the optical member is so short that changes in the states ofinterferometer and oil are considered to be substantially negligible.Therefore, such a method can measure the wavefront aberration with ahigher accuracy.

[0166] The principle of measuring the wavefront aberration of an opticalmember according to the above-mentioned embodiment will be explained.First, the wavefront aberration W depending on the inner homogeneity ofthe optical member is expressed as

W=Ws+Wa  (14)

[0167] when classified according to elements constituting the same,assuming Ws to be the rotationally symmetric element, and Wa to be thenon-rotationally symmetric element (the total of the odd rotationallysymmetricelement, even rotationally symmetric element, and residual). Asshown in FIGS. 7A and 7B, respective wavefront data items measured atindividual angles while rotating the optical member by 360°/n arereferred to as Dw(1), Dw(2), . . . , Dw(n), and respective wavefrontaberrations (inner homogeneity values) of the optical member at theindividual angles are referred to as W(1), W(2), . . . , W(n). Here,since the rotationally symmetric element is defined as

Ws=ΣW(i)/n,  (15)

W(i)=Ws+Wa(i)  (16)

[0168] from expression (14). Therefore,

ΣW(i)/n=ΣWs/n+ΣWa(i)/n,

[0169] which becomes

ΣWa(i)/n=ΣW(i)/n−ΣWS/n=Ws=0

[0170] by transposing terms, namely, the value of the non-rotationallysymmetric element averaged by rotation becomes zero. Letting S be thewavefront aberration of plane-parallel plate members, K be the wavefrontaberration of the measurement optical system of the interferometer, andM be the wavefront aberration of the reflecting surface, therotationally averaged data becomes

ΣDw(i)/n=ΣW(i)/n+S+K+M=Ws+E+O  (17)

[0171] according to the definition of expression (15). From expression(16), the wavefront data Dw(1) of the optical member in the direction of0° becomes

Dw(1)=W(1)+S+K+M=Ws+Wa(1)+E+O.  (18)

[0172] Hence, when the expression of rotationally averaged data (17) issubtracted from expression (18),

Dw(1)−ΣD(i)/n=Wa(1).

[0173] Namely, the non-rotationally symmetric element Wa is determined.

[0174] Next, letting Dw(x) be the wavefront data obtained by shiftingthe optical member sidewise as shown in FIGS. 8A and 8B, and Ws(x) andWa(x) be the rotationally symmetric and non-rotationally symmetricelements of inner homogeneity of the optical member, respectively, atthis time,

Dw(x)=Ws(x)+Wa(x)+E+O.  (19)

[0175] When this wavefront data Dw(x) is subtracted from the wavefrontdata Dw(1) in the direction of 0° (no shift state),

Dw(1)−Dw(x)=(Ws+Wa)−(Ws(x))

[0176] from expressions (18) and (19). Here, since Wa is known, Wa(x)determined based thereon is also known. By transposing unknown terms tothe left side, and measurement data terms to the right side,

Ws−Ws(x)=Dw(1)−Dw(x)−(Wa−Wa(x)).

[0177] Since Ws(x) is determined by using the fact that the rotationallysymmetric element Ws is data superposed upon sidewise shifting whereasthe rotationally symmetric element comprises concentrically distributedcontour lines, this term is also transposed to the right side, whereby

Ws=Dw(1)−Dw(x)−(Wa−Wa(x))+Ws(x),

[0178] which determines the rotationally symmetric element Ws. Namely,since the data structure of the wavefront aberration inherent in theoptical member is as shown in expression (14), the wavefront aberration(inner homogeneity) inherent in the optical member is determined.

[0179] Though the accuracy of measurement becomes higher as the numberof operations of obtaining wavefront data by rotating the optical memberincreases in principle, it takes a longer time for measurement, wherebythe states of interferometer and oil fluctuate more, thus causing themeasurement accuracy to decrease. Therefore, it is consideredappropriate if the number of operations is 3 to 4 in actual measurement.The number of operations may be 2 in order to carry out measurement in ashort period of time. In this case, it is not necessary for theirpositional relationship to be diagonal (e.g., 0° and 180°), but may be acombination of 0° and 60°, for example.

[0180] Though the measurement accuracy becomes higher as the amount bywhich the optical member is shifted sidewise is greater in principle,the state in which the optical member is supported and the like maychange, thereby causing the measurement accuracy to decrease. Therefore,the sidewise shifting amount should not be enhanced more than necessary,and is considered appropriate if it is about 10% of the diameter of theoptical member.

[0181] The method of expanding thus determined wavefront aberration toan orthogonal function system such as a Zernike cylindrical function isas explained above.

[0182] Next, a method of making a favorable optical member will beexplained with reference to silica glass made by a method known asdirect method by way of example.

[0183] In the direct method, which is one of silica glass synthesizingmethods, a silicon compound gas diluted with a carrier gas is jetted outfrom a multitube burner made of silica glass in a furnace. At this time,oxygen and hydrogen gases are also jetted out from the multitube burnermade of silica glass and are burned, so that high-purity silica glass isdeposited while in a transparent state onto a target, whereby an ingotis obtained. Examples of silicon compound gas include chlorine compounds(e.g., SiCl₄ and the like), various organic silicon compounds, fluorinecompounds (e.g., SiF₄ and the like), and so forth. Upon synthesis, thetarget is descended while being rotated and periodically swung at thesame time, so that the upper surface of the ingot is always positionedconstant with respect to the burner.

[0184] Also, the temperature in the upper part of the ingot is measured,and the burner and ingot are moved relative to each other within a planeaccording to the result of measurement. This is effected in order tooptimize the refractive index homogeneity of the silica glass ingot bycontrolling the temperature distribution pattern in the upper part ofthe ingot caused by the burner form, jetted gas amount, and the like incombination with the temperature distribution pattern caused by therelative movement between the burner and ingot.

[0185] A characteristic feature of the direct method lies in thatmembers having a higher resistance to excimer laser and a greaterdiameter can be obtained thereby in comparison with other methods. Therefractive index homogeneity of the silica glass is determined byimpurities and the density distribution. Examples of impurities includeOH, Cl, F, metal impurities, dissolved gases, and the like. In the caseof direct method using a chlorine compound as a material gas, forexample, OH contained by several hundred ppm or more and, secondly, Clcontained by several ten ppm are considered predominant.

[0186] As the density distribution, that caused by thermal history ispredominant. Since the refractive index distribution is determined bysuch factors, a manufacturing method which always keeps the geometriccenter position in each of steps of (1) synthesis, (2) heat treatmentfor homogenizing and shaping, (3) annealing for excluding strain, and(4) machining such as cutting/rounding is necessary in order to obtainsilica glass having a favorable refractive index homogeneity. An exampleof the manufacturing method will be shown in the following.

[0187] Since silica glass is synthesized while rotating the target, theimpurity concentration distribution, the physical property distribution,and the refractive index distribution based thereon in the ingotmanufactured are macroscopically symmetrical about the center. FIG. 9shows steps of yielding an optical member from thus obtained ingot.First, the ingot 21 is cut into a plurality of columnar members 22.Since the side face of the columnar members 22 is the side face of ingotitself, the center of the columnar members 22 becomes the center of theingot 21. When the center of the columnar member 22 is marked on a crosssection so as to become a reference for subsequent machining such ascutting and rounding, the center axis of the ingot 21 and the centeraxis of silica glass components coincide with each other, whereby lenseswith amacroscopically favorable symmetry about the center can beexpected to be made eventually.

[0188] As mentioned above, the refractive index distribution of silicaglass is determined by the density distribution caused by impurities andthermal history, which can be controlled according to synthesizingconditions. To this aim, it is necessary that materials, oxygen,hydrogen, exhaust flow rate, target rpm, descending rate, and the likewhich are influential in fluctuations of synthesizing conditions haveconfigurations which are controllable with a high accuracy. For aligningthe respective centers of the furnace, burner, and ingot, they arepositioned with reference to the optical axis of laser light.

[0189] The columnar member 22 is obtained from the ingot 21 synthesizedby such a method, and its upper and lower faces are subjected to shavingand then are ground to a high precision, thus yielding an opticalmember. The refractive index distribution of such an optical member ismeasured by an interferometer; each of the rotationally symmetric,odd-symmetric, and even-symmetric elements of wavefront aberration isseparated into lower-, middle-, and higher-order elements; and theresidual, the residual RMS value, and the like are determined. Then, forreducing these values, synthesizing conditions are adjusted, and thesynthesis is carried out again. For example, control of the gas flowrate of the burner or control of the condition under which the burnerand the target are moved relative to each other at the time of synthesisis carried out.

[0190] Also, in the heat treatment after the synthesis, placement ofSiO₂ powder or mass on the upper/lower side or on the side face forregulating the heat dissipation at the time of temperature drop,adjustment of temperature descending rate at the time of annealing,adjustment of holding pressure at the time of HIP (hot isostaticpressing) after annealing, and the like can control each of theabove-mentioned values. However, the symmetry about the center will belost if heat treatment is carried out at a high temperature exceeding1700° C.

[0191] These methods can adjust the refractive index distribution, so asto yield desirable optical performances. Such an optical member 22 isrounded, so as to yield a silica glass member 23 to be processed into alens. Subsequently, processing such as shaving and grinding is carriedout, so as to make a projection lens 24. The foregoing steps makeoptical elements such as lenses, prisms, and reflecting mirrors havingvarious forms, which are appropriately combined together and assembledinto a lens barrel, so as to make a projection optical system, and thensuch a projection optical system is assembled into an excimer laserstepper.

[0192]FIG. 10 shows a conceptual view of the excimer laser stepper. Inthis drawing, 8 is a projection optical system, 1 is an excimer laserlight source, 2 is an illumination optical system, 3 is a mask, and 9 isa silicon wafer for projection under demagnification. Provided as thelight source 1 for emitting illumination light in a UV region is F₂laser (oscillation center wavelength at 157.6 nm). The light emittedfrom the light source 1 illuminates, at a uniform illuminance, by way ofthe illumination optical system 2, the mask 3 formed with apredetermined pattern.

[0193] In the optical path extending from the light source 1 to theillumination optical system 2, one or a plurality of mirrors for bendingthe optical path as necessary are disposed. The illumination opticalsystem 2 comprises an optical integrator, a field stop, a field stopoptical system, and the like. The optical integrator forms apredetermined surface light source, for example, by a flyeye lens, aninternal reflection type integrator, or the like. The field stop is usedfor defining the size/form of the illumination area on the mask 3,whereas the field stop optical system is used for projecting the fieldstop image onto the mask.

[0194] The optical path between the light source 1 and the illuminationoptical system 2 is tightly sealed with a casing (not depicted), whereasthe space from the light source 1 to the lens closest to the mask in theillumination optical system 2 is filled with an inert gas exhibiting alow absorptivity with respect to the exposure light.

[0195] By way of a mask holder 4, the mask 3 is held on a mask stage 5so as to become parallel to the XY plane. The mask 3 is formed with apattern to be transferred. In the whole pattern area, a rectangular(slit-like) region having a shorter side along the X direction and alonger side along the Y direction is illuminated.

[0196] The mask stage 5 is two-dimensionally movable along the masksurface (i.e., XY plane), whereas its positional coordinates aremeasured by an interferometer 7 using a mask movable mirror 6, so as toeffect positional control.

[0197] The light transmitted through the pattern formed in the mask 3forms a mask pattern image onto the wafer 9, which is a photosensitivesubstrate, by way of the projection optical system 8. By way of a waferholder 10, the wafer 9 is held on a wafer stage 11 so as to becomeparallel to the XY plane. The wafer stage 11 is two-dimensionallymovable along the XY plane such that a rectangular exposure area havinga shorter side along the X direction and a longer side along the Ydirection on the wafer 9 optically corresponds to the rectangularillumination area on the mask 3. Positional coordinates of the waferholder 10 are measured by an interferometer 13 using a wafer movablemirror 12, so as to effect positional control.

[0198] The inside of the projection optical system 8 is constructed soas to keep a hermetic state, whereas the space there with in is filledwith an inert gas.

[0199] Disposed within the narrow optical path between the illuminationoptical system 2 and the projection optical system 8 are the mask 3, themask stage 5, and the like. A casing (not depicted) tightly surroundingthe mask 3, the mask stage 5, and the like is filled with an inert gas.

[0200] As such, an atmosphere which hardly absorbs exposure light isformed throughout the optical path extending from the light source 1 tothe wafer 9.

[0201] As mentioned above, the illumination area on the mask 3illuminated by way of the projection optical system 8 and the exposurearea on the wafer 9 are in a rectangular form having a shorter sidealong the X direction. Therefore, while carrying out positional controlof the mask 3 and wafer 9 by using a driving system, interferometers (7,13), and the like, the mask stage 5 and the wafer stage 11 are moved(scanned) in synchronization with each other along the shorter sidedirection of the rectangular illumination area and exposure area, i.e.,X direction, whereby the mask pattern is exposed in a scanning fashionto a region having a width identical to the longer side of the exposurearea and a length corresponding to the moving (scanning) amount of thewafer 9.

[0202] Such a configuration enables photolithography which can yieldfine and vivid patterns. The present invention can yield a patternhaving a line width of 0.3 μm or shorter.

EXAMPLES

[0203] In the following, the present invention will be explained morespecifically with reference to Examples, which do not restrict thepresent invention.

EXAMPLE 1

[0204] Using the above-mentioned direct method, a plurality of ingotseach having a diameter of 500 mm and a length of 800 mm were made, anddisk-shaped test pieces were horizontally cut out from these ingots. Atthis time, the center of rotation of ingots and the center of disks werealigned with each other. For excluding strain and homogeneityadjustment, the test pieces were set at the center of an annealingfurnace having a temperature distribution symmetric about the center andwere subjected to annealing while rotating (held at 1000° C. for 24hours, then cooled to 500° C. with a temperature gradient of −10°C./min, and left to cool thereafter).

[0205] Further, from these disks, disk-shaped optical members eachhaving a diameter of 300 mm and a thickness of 60 mm were extracted byusing a core drill, and their upper and lower faces were ground. At thistime, the center of rotation of the ingot and the center of each diskwere aligned with each other. For evaluating the refractive indexhomogeneity of this member, it is necessary to know the tilted componentof refractive index. This is because of the fact that the tiltedcomponent of refractive index is hard to measure directly with aninterferometer. Therefore, two prism-shaped samples were taken out fromboth ends of this member in the diametric direction, respectively, andthe refractive index of each sample was measured with an accuracy on theorder of 10⁻⁷ according to the minimum deviation method by using ahighly accurate spectrometer. As a result, the refractive indexdifference between the two samples was not greater than the measurementlimit, i.e., −10⁻⁷ or less.

[0206] Subsequently, the disk-shaped member was set to a Fizeau typeinterferometer, using an He-Ne laser at a wavelength of 633 nm as alight source, for measuring flat optical members, and its wavefrontaberration was measured in 100×100 mesh measurement points (ρ,θ) by theoil-on-plate method. Using thus measured wavefront aberration data, thewavefront aberration profile was fitted (applied) to a Zernikecylindrical function system Zn (ρ,θ) to terms where n=0 to 80. Namely,from a plurality of measurement data items, expansion coefficients of C₀to C₈₀ were determined by the least-squares method.

[0207] Then, thus determined expansion coefficients were put intoexpression (1), so as to calculate W(ρ,θ) for each measurement point.Next, thus determined expansion coefficients were put into expressions(5) to (13), so as to calculate the lower-order W_(rot), lower-orderW_(odd), lower-order W_(evn), middle-order W_(rot), middle-orderW_(odd), middle-order W_(evn), higher-order W_(rot), higher-orderW_(odd), and higher-order W_(evn) for each measurement point; and fromthese values, the lower-order r_(rot), lower-order r_(odd), lower-orderr_(evn), middle-order r_(rot), middle-order r_(odd), middle-orderr_(evn)higher-order r_(rot), higher-order r_(odd), and higher-orderr_(evn) were calculated. Also, for each measurement point, thedifference between the actual measurement data and W(ρ,θ) calculatedaccording to expression (1) by substitution was determined, so as toyield a residual, and the residual RMS value was calculated from thesevalues. As such, RMS values according to the Zernike cylindricalfunction system where n=0 to 80 were determined in the disk-shapedoptical members made from the ingots manufactured under variousconditions.

[0208] Then, the disk-shaped optical members were sorted into aplurality of classes according to the magnitude of thus determined RMSvalues. Thereafter, using only the disk-shaped optical members sortedinto one class at first, a plurality of kinds of lenses necessary forconstructing a projection optical system for use in a photolithographyexposure apparatus employing an ArF excimer laser as a light source wereobtained by processing. Subsequently, these lenses were combinedtogether so as to construct the projection optical system, therebyassembling a projection optical system constituted by the opticalmembers corresponding to this class. For other classes, respectiveprojection optical systems constituted by optical members correspondingto these classes were assembled successively as mentioned above. Thus,the projection optical systems constituted by the respective opticalmembers corresponding to the individual classes were produced, andwavefront aberrations of these projection optical systems were evaluatedwith a Fizeau type interferometer.

[0209] Here, the principle of wavefront aberration caused by a Fizeautype interferometer for measuring optical systems will be explained withreference to FIG. 11. Alight source 31 is required to use light havingthe same wavelength as that actually employed in the exposure apparatus.Here, an ArF excimer laser is used as the light source 31. The luminousflux emitted from the light source 31 is reflected by (or transmittedthrough) a half prism 32, so as to be made incident on a Fizeau lens 33.A part of the luminous fluxincident on the Fizeau lens 33 is reflectedby are ference surface 33 a of the Fizeau lens, so as to becomereference light, which travels back the incoming path to return to thehalf prism 32. The other part of luminous flux incident on the Fizeaulens 33 is transmitted through the reference surface 33 a, so as tobecome measurement light. The measurement light passes through a setprojection optical system 37 and is reflected by a spherical mirror 34mounted on an XY stage 35, so as to travel back the incoming path toreturn to the half prism 32. The reference light and measurement lightincident on the half prism 32 are transmitted through (or reflected by)the half prism 32, so as to form an image of the spherical mirror 34 onan imaging device 36.

[0210] When the projection optical system 37 has no aberration, themeasurement light is incident on individual points of the sphericalmirror 34 in the same phase, and returns to individual points of thereference surface 33 a of the Fizeau lens in the same phase. As aconsequence, the reference light and measurement light have the samephase difference at each point on the imaging device 36, whereby theimage of the spherical mirror 34 yields a uniform intensitydistribution. When the projection optical system 37 has an aberration,by contrast, the phase difference between reference light andmeasurement light varies among the individual points on the imagingdevice 36, where by interference fringes are seen as an image of thespherical mirror 34. Since the measurement light has passed through theprojection optical system 37 twice, the wavefront aberration W of theprojection optical system 37 can be determined by dividing the phasedifference of interference fringes by 2.

[0211] Dividing the imaging device 36 into elements of 100×100 mesh, thevalue of wavefront aberration Win each element is determined, and itsRMS value is calculated, so as to evaluate the optical performance ofthe projection optical system 37.

[0212] The following Table 1 shows the RMS values of elements of thedisk-shaped optical members used for lenses constituting the individualprojection optical systems, results of determination of opticalperformances, wavefront aberration RMS, and second- and fourth-orderresidual RMS and PV values according to a conventional evaluatingmethod. Namely, the RMS values of individual elements of the disk-shapedoptical member used for a plurality of lenses constituting each sampleNo. of projection optical system are listed in the columns oflower-order r_(rot), lower-order r_(odd), lower-order r_(evn),middle-order r_(rot), middle-order r_(odd), middle-order r_(evn),higher-order r_(rot), higher-order r_(odd), higher-order r_(evn), andresidual RMS value, whereas the results of evaluation of opticalperformances as the projection optical system and the wavefrontaberration RMS value are shown in the columns of optical performance andwavefront aberration RMS, respectively. Also, the second- andfourth-order residual RMS and PV values of each disk-shaped opticalmember were determined according to the conventional evaluating methoddescribed in Japanese Patent Application Laid-Open No. HEI 8-5505, andthus obtained results are shown in the columns of second/fourth-orderRMS and second/fourth-order PV, respectively. TABLE 1 (x λ) 2nd/4th-2nd/4th- Sam- Lower- Lower- Lower- Middle- Middle- Middle- Higher-Higher- Higher- Wavefront order order ple order order order order orderorder order order order Residual Optical aberration residual residualNo. rrot rodd revn rrot rodd revn rrot rodd revn RMS performance RMS RMSPV 1 0.002 0.0015 0.002 0.001 0.001 0.001 0.0002 0.0002 0.0002 0.0002 ⊚0.007 0.001 0.011 2 0.003 0.0025 0.003 0.002 0.002 0.002 0.0004 0.00050.0005 0.0004 ⊚ 0.008 0.003 0.015 3 0.008 0.006 0.007 0.004 0.003 0.0040.001 0.0008 0.0008 0.001 ⊚ 0.01 0.004 0.016 4 0.015 0.01 0.015 0.0060.004 0.003 0.002 0.002 0.001 0.003 ⊚ 0.013 0.005 0.018 5 0.02 0.02 0.020.008 0.008 0.008 0.003 0.003 0.003 0.004 ⊚ 0.15 0.004 0.022 6 0.02 0.020.02 0.01 0.009 0.008 0.003 0.003 0.003 0.004 ∘ 0.18 0.004 0.023 7 0.040.03 0.03 0.008 0.008 0.007 0.004 0.003 0.003 0.005 ∘ 0.02 0.005 0.024 80.06 0.06 0.06 0.02 0.02 0.02 0.005 0.005 0.005 0.006 ∘ 0.025 0.0050.024 9 0.07 0.05 0.06 0.02 0.02 0.02 0.007 0.005 0.006 0.007 Δ 0 040.005 0.024 10 0.06 0.05 0.06 0.03 0.02 0.03 0.005 0.007 0.007 0.006 Δ 005 0.006 0.026 11 0.08 0.07 0.06 0.03 0.02 0.02 0.005 0.004 0.005 0.006Δ 0 05 0.006 0.025 12 0.06 0.07 0.06 0.03 0.03 0.02 0.006 0.007 0.0050.008 x 0.07 0.005 0.024 13 0.08 0.06 0.08 0.04 0.03 0.03 0.007 0.0060.006 0.008 x 0 08 0.005 0.024 14 0.08 0.08 0.07 0.04 0.04 0.05 0.0080.007 0.009 0.009 x 0 1 0.007 0.03

[0213] The results shown in Table 1 have indicated that, with respect tothe light source wavelength λ, optical members whose lower-order r_(rot)is 0.06λ or less, lower-order r_(odd) is 0.06λ or less, and lower-orderr_(evn) is 0.06λ or less, or middle-order r_(rot) is 0.02λ or less,middle-order r_(odd) is 0.02λ or less, and middle-order r_(evn) is 0.02λor less, or higher-order r_(rot) is 0.005λ or less, higher-order r_(odd)is 0.005λ or less, and higher-order r_(evn) is 0.005λ or less, orresidual RMS is 0.006λ or less yield a wavefront aberration RMS of 0.05λor less, thus attaining favorable optical performances forphotolithography.

[0214] It has also been seen that, with respect to the light sourcewavelength λ optical members whose lower-order r_(rot) is 0.06λ or less,lower-order r_(odd) is 0.06λ or less, and lower-order r_(evn) is 0.06λor less, and middle-order r_(rot) is 0.02λ or less, middle-order r_(odd)is 0.02λ or less, and middle-order r_(evn) is 0.02λ or less, andhigher-order r_(rot) is 0.005λ or less, higher-order r_(odd) is 0.005λor less, and higher-order r_(evn) is 0.005λ or less, and residual RMS is0.006λ or less yield a wavefront aberration RMS of 0.025λ or less, thusattaining further favorable imaging performances for photolithography.

[0215] It has also been seen that optical members whose lower-orderr_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ or less, andlower-order r_(evn) is 0.02λ or less, or middle-order r_(rot) is 0.008λor less, middle-order r_(odd) is 0.008λ or less, and middle-orderr_(evn) is 0.008λ or less, or higher-order r_(rot) is 0.003λ or less,higher-order r_(odd) is 0.003λ or less, and higher-order r_(evn) is0.003λ or less, or residual RMS is 0.004λ or less yield a wavefrontaberration RMS of 0.025λ or less, thus attaining further favorableoptical performances for photolithography, and are favorable as opticalmembers for projection optical systems in particular.

[0216] It has also been seen that optical members whose lower-orderr_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ or less, andlower-order r_(evn) is 0.02λ or less, and middle-order r_(rot) is 0.008λor less, middle-order r_(odd) is 0.008λ or less, and middle-orderr_(evn) is 0.008λ or less, and higher-order r_(rot) is 0.003λ or less,higher-order r_(odd) is 0.003λ or less, and higher-order r_(evn) is0.003λ or less, and residual RMS is 0.004λ or less yield a wavefrontaberration RMS of 0.015λ or less, thus attaining further favorableoptical performances for photolithography, and are favorable as opticalmembers for projection optical systems in particular.

[0217] Further, the results of samples No. 12 and No. 13, for example,have indicated that, even when disk-shaped optical members exhibitingsufficiently low second- and fourth-order residual RMS and PV valuesaccording to the conventional evaluating method are processed intolenses so as to constitute projection optical systems, their wavefrontaberration RMS does not always exhibit small values, i.e., their opticalperformances do not always become favorable. On the contrary, theresults of samples No. 10 and No. 11, for example, have indicated that,even when disk-shaped optical members exhibiting relatively largesecond- and fourth-order residual RMS and PV values according to theconventional evaluating method are processed into lenses so as toconstitute projection optical systems, their wavefront aberration RMSmay exhibit small values, i.e., their optical performances may becomefavorable.

EXAMPLE 2

[0218] Using the wavefront aberration data measured from individualoptical members (sample Nos. 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, and 14),the wavefront aberration profile was fitted (applied) to a Zernikecylindrical function system Zn(ρ,θ) to terms where n=0 to 35. Namely,from a plurality of measurement data items, expansion coefficients of C₀to C₃₅ were determined by the least-squares method.

[0219] Then, thus determined expansion coefficients were put intoexpression (1), so as to calculate W(ρ,θ) for each measurement point.Next, thus determined expansion coefficients were put into expressions(5) to (10), so as to calculate the lower-order W_(rot), lower-orderW_(odd), lower-order W_(evn), middle-order W_(rot), middle-orderW_(odd), and middle-order W_(evn); and from these values, thelower-order r_(rot), lower-order r_(odd), lower-order r_(evn)middle-order r_(rot), middle-order r_(odd), and middle-order r_(evn)were calculated. Also, for each measurement point, the differencebetween the actual measurement data and W(ρ,θ) calculated by expression(1) by substitution was determined, so as to yield a higher-orderresidual, and the residual RMS value was calculated from these values.As such, RMS values according to the Zernike cylindrical function systemwhere n=0 to 35 were determined in the disk-shaped optical members ofsample Nos. 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, and 14 in Example 1.

[0220] The following Table 2 shows the RMS values of elements of thedisk-shaped optical members used for lenses constituting the individualprojection optical systems, results of determination of opticalperformances, wavefront aberration RMS, and second- and fourth-orderresidual RMS and PV values according to the conventional evaluatingmethod. TABLE 2 (x A) Higher- 2nd/4th- 2nd/4th- Lower- Lower- Lower-Middle- Middle- Middle- order Wavefront order order Sample order orderorder order order order residual Optical aberration residual residualNo. rrot rodd revn rrot rodd revn RMS performance RMS RMS PV 1 0.0030.0025 0.003 0.002 0.002 0.002 0.0005 ⊚ 0.008 0.003 0.015 2 0.008 0.0060.007 0.004 0.003 0.004 0.0008 ⊚ 0.01 0.004 0.016 3 0.015 0.01 0.0150.006 0.004 0.003 0.002 ⊚ 0.013 0.005 0.018 4 0.02 0.02 0.02 0.008 0.0080.008 0.004 ⊚ 0.015 0.004 0.022 5 0.02 0.02 0.02 0.01 0.009 0.008 0.006∘ 0.018 0.004 0.023 6 0.04 0.03 0.03 0.008 0.009 0.009 0.004 ∘ 0.020.005 0.024 7 0.06 0.06 0.06 0.02 0.02 0.02 0.01 ∘ 0.025 0.005 0.024 80.07 0.05 0.06 0.02 0.02 0.02 0.015 Δ 0.04 0.005 0.024 9 0.06 0.05 0.060.03 0.02 0.03 0.01 Δ 0.05 0.006 0.026 10 0.06 0.07 0.06 0.03 0.03 0.020.02 x 0.07 0.005 0.024 11 0.08 0.08 0.07 0.04 0.04 0.05 0.0325 x 0.10.007 0.03

[0221] The results shown in Table 2 have indicated that, with respect tothe light source wavelength λoptical members whose lower-order r_(rot)is 0.06λ or less, lower-order r_(odd) is 0.06λ or less, and lower-orderr_(evn) is 0.06λ or less, or middle-order r_(rot) is 0.02λ or less,middle-order r_(odd) is 0.02λ or less, and middle-order r_(evn) is 0.02λor less, or higher-order residual RMS is 0.01λ or less yield a wavefrontaberration RMS of 0.05λ or less, thus attaining favorable opticalperformances for photolithography.

[0222] It has also been seen that, with respect to the light sourcewavelength λ optical members whose lower-order r_(rot) is 0.06λ or less,lower-order r_(odd) is 0.06λ or less, and lower-order r_(evn) is 0.06λor less, and middle-order r_(rot) is 0.02λ or less, middle-order r_(odd)is 0.02λ or less, and middle-order r_(evn) is 0.02λ or less, andhigher-order residual RMS is 0.01λ or less yield a wavefront aberrationRMS of 0.025λ or less, thus attaining more favorable opticalperformances for photolithography.

[0223] It has also been seen that optical members whose lower-orderr_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ or less, andlower-order r_(evn) is 0.02λ or less, or middle-order r_(rot) is 0.008λor less, middle-order r_(odd) is 0.008λ or less, and middle-orderr_(evn) is 0.008λ or less, or higher-order residual RMS is 0.004λ orless yield a wavefront aberration RMS of 0.025λ or less, thus attainingmore favorable optical performances for photolithography, and arefavorable as optical members for projection optical systems inparticular.

[0224] It has also been seen that optical members whose lower-orderr_(rot) is 0.02λ or less, lower-order r_(odd) is 0.02λ or less, andlower-order r_(evn) is 0.02λ or less, and middle-order r_(rot) is 0.008λor less, middle-order r_(odd) is 0.008λ or less, and middle-orderr_(evn) is 0.008or less, and higher-order residual RMS is 0.004λ or lessyield a wavefront aberration RMS of 0.015λ or less, thus attainingfurther favorable optical performances for photolithography, and arefavorable as optical members for projection optical systems inparticular.

[0225] Further, the results of sample No. 12, for example, haveindicated that, even when a disk-shaped optical member exhibitingsufficiently low second- and fourth-order residual RMS and PV valuesaccording to the conventional evaluating method is processed into a lensso as to constitute a projection optical system, its wavefrontaberration RMS does not always exhibit a small value, i.e., its opticalperformances do not always become favorable. On the contrary, theresults of sample No. 10, for example, have indicated that, even when adisk-shaped optical member exhibiting relatively large second- andfourth-order residual RMS and PV values according to the conventionalevaluating method is processed into a lens so as to constitute aprojection optical system, its wavefront aberration RMS may exhibit asmall value, i.e., its optical performances may become favorable.

[0226] Though the above-mentioned embodiment of the present inventionseparates the measured wavefront aberration into rotationally symmetric,odd-symmetric, and even-symmetric components, and then separates eachcomponent into lower-, middle-, and higher-order elements, this ordermay be reversed. Namely, totally the same results are obtained when themeasured wavefront aberration is separated into lower-, middle-, andhigher-order elements, and then each element is separated intorotationally symmetric, odd-symmetric, and even-symmetric components.Thus, the present invention encompasses not only the former procedurebut also the latter procedure.

Comparative Example

[0227] Using the direct method similar to that in Example 1, a pluralityof columnar ingots each having a diameter of 200 mm and a length of 400mm were made. In the state heated to the softening temperature, thusobtained ingot was pressed to collapse while twisting its end facesleftward and rightward, whereby a test piece having a diameter of about500 mm and a thickness of about 60 mm was formed eventually. Then, forexcluding strain and homogeneity adjustment, the test piece was set atthe center of an annealing furnace having a temperature distributionsymmetric about the center and were subjected to annealing whilerotating (held at 1000° C. for 24 hours, then cooled to 500° C. with atemperature gradient of −10° C./min, and left to cool thereafter).

[0228] Further, from these disks, disk-shaped optical members eachhaving a diameter of 300 mm and a thickness of 60 mm were extracted byusing a core drill, and their upper and lower faces were ground.

[0229] Thereafter, using a Fizeau type interferometer for measuring flatoptical members as in Example 1, lower-order r_(rot), lower-orderr_(odd), lower-order r_(evn), middle-order r_(rot), middle-orderr_(odd), middle-order r_(evn), higher-order r_(rot), higher-orderr_(odd), higher-order r_(evn), and residual RMS value were calculated.As such, in the disk-shaped optical members made of the ingotsmanufactured under the above-mentioned condition, RMS values accordingto a Zernike cylindrical function system where n=0 to 80 weredetermined.

[0230] Thus obtained RMS values of individual elements yielded largevalues in higher- and lower-order elements in particular, and largevalues in the non-rotationally symmetric element as well.

[0231] Then, in the same manner as Example 1 except that suchdisk-shaped optical members were used, lenses were made by processing,so as to assemble projection optical systems. Thus obtained projectionoptical systems yielded very large wavefront aberration RMS values uponmeasurement, whereby it was found that they failed to yield favorableoptical performances for photolithography.

[0232] Industrial Applicability

[0233] As explained in the foregoing, the present invention makes itpossible to evaluate the refractive index homogeneity of an opticalmember more accurately, whereby a photolithography optical member havinga high refractive index homogeneity and a high quality can be providedmore reliably. Therefore, by using such an optical member, the presentinvention can make not only a high-precision photolithography projectionoptical system but also a high-performance photolithography exposureapparatus reliably with a high efficiency.

1. A method of evaluating a refractive index homogeneity of an opticalmember for photolithography, said method comprising: a measurement stepof transmitting light having a predetermined wavelength λ through saidoptical member so as to measure a wavefront aberration; a Zernikefitting step of expanding thus measured wavefront aberration into apolynomial of a Zernike cylindrical function system; a first separatingstep of separating individual components of said polynomial into arotationally symmetric element, an odd-symmetric element, and aneven-symmetric element; and a second separating step of separatingindividual components of said polynomial into a plurality of partsaccording to a degree thereof.
 2. An evaluating method according toclaim 1, wherein individual components of said polynomial are separatedinto three parts of lower, middle, and higher orders in said secondseparating step.
 3. An evaluating method according to claim 2, whereinsaid three parts of lower, middle, and higher orders are terms where n=4to 8, n=9 to 35, and n>35 in the polynomial of the Zernike cylindricalfunction system, respectively, whereas a term where n=0 to 3 is unusedfor evaluation.
 4. An evaluating method according to claim 1, wherein,in said first and second separating steps, individual components of saidpolynomial are classified such that a rotationally symmetric element, anodd-symmetric element, and an even-symmetric element in a term where n=4 to 8 become a lower-order rotationally symmetric element, alower-order odd-symmetric element, and a lower-order even-symmetricelement, respectively; a rotationally symmetric element, anodd-symmetric element, and an even-symmetric element in a term where n=9to 35 become a middle-order rotationally symmetric element, amiddle-order odd-symmetric element, and a middle-order even-symmetricelement, respectively; and a rotationally symmetric element, anodd-symmetric element, and an even-symmetric element in a term wheren=36 to 80 become a higher-order rotationally symmetric element, ahigher-order odd-symmetric element, and a higher-order even-symmetricelement, respectively; and a term where n>80 becomes a residual in saidpolynomial; said evaluating method further comprising: an RMS valuecalculating step of calculating an RMS value of each of said lower-orderrotationally symmetric element, lower-order odd-symmetric element,lower-order even-symmetric element, middle-order rotationally symmetricelement, middle-order odd-symmetric element, middle-order even-symmetricelement, higher-order rotationally symmetric element, higher-orderodd-symmetric element, higher-order even-symmetric element, andresidual; and an evaluating step of evaluating whether thus calculatedRMS value satisfies a predetermined condition or not.
 5. An evaluatingmethod according to claim 4, wherein said evaluating step evaluateswhether at least one of the following conditions (a₁), (b₁), (c₁), and(d₁) is satisfied or not: (a₁) each of the respective RMS values of thelower-order rotationally symmetric element, lower-order odd-symmetricelement, and lower-order even-symmetric element is 0.06λ or less; (b₁)each of the respective RMS values of the middle-order rotationallysymmetric element, middle-order odd-symmetric element, and middle-ordereven-symmetric element is 0.02λ or less; (c₁) each of the respective RMSvalues of the higher-order rotationally symmetric element, higher-orderodd-symmetric element, and higher-order even-symmetric element is 0.005λor less; and (d₁) the RMS value of the residual is 0.006λ or less.
 6. Anevaluating method according to claim 4, wherein said evaluating stepevaluates whether at least one of the following conditions (a₂), (b₂),(c₂), and (d₂) is satisfied or not: (a₂) each of the respective RMSvalues of the lower-order rotationally symmetric element, lower-orderodd-symmetric element, and lower-order even-symmetric element is 0.02λor less; (b₂) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.008λ or less; (c₂) each of therespective RMS values of the higher-order rotationally symmetricelement, higher-order odd-symmetric element, and higher-ordereven-symmetric element is 0.003λ or less; and (d₂) the RMS value of theresidual is 0.004λ or less.
 7. An evaluating method according to claim5, wherein said evaluating step evaluates whether all of said conditions(a₁), (b₁), (c₁), and (d₁) are satisfied or not.
 8. An evaluating methodaccording to claim 6, wherein said evaluating step evaluates whether allof said conditions (a₂), (b₂), (c₂), and (d₂) are satisfied or not. 9.An evaluating method according to claim 1, wherein, in said first andsecond separating steps, individual components of said polynomial areclassified such that a rotationally symmetric element, an odd-symmetricelement, and an even-symmetric element in a term where n=4 to 8 become alower-order rotationally symmetric element, a lower-order odd-symmetricelement, and a lower-order even-symmetric element, respectively; arotationally symmetric element, an odd-symmetric element, and aneven-symmetric element in a term where n=9 to 35 become a middle-orderrotationally symmetric element, a middle-order odd-symmetric element,and a middle-order even-symmetric element, respectively; and a termwhere n>35 becomes a higher-order residual in said polynomial; saidevaluating method further comprising: an RMS value calculating step ofcalculating an RMS value of each of the lower-order rotationallysymmetric element, lower-order odd-symmetric element, lower-ordereven-symmetric element, middle-order rotationally symmetric element,middle-order odd-symmetric element, middle-order even-symmetric element,and higher-order residual; and an evaluating step of evaluating whetherthus calculated RMS value satisfies a predetermined condition or not.10. An evaluating method according to claim 9, wherein said evaluatingstep evaluates whether at least one of the following conditions (a₃),(b₃), and (c₃) is satisfied or not: (a₃) each of the respective RMSvalues of the lower-order rotationally symmetric element, lower-orderodd-symmetric element, and lower-order even-symmetric element is 0.06λor less; (b₃) each of the respective RMS values of the middle-orderrotationally symmetric element, middle-order odd-symmetric element, andmiddle-order even-symmetric element is 0.02λ or less; and (c₃) the RMSvalue of the higher-order residual is 0.01λ or less.
 11. An evaluatingmethod according to claim 9, wherein said evaluating step evaluateswhether at least one of the following conditions (a₄), (b₄), and (c₄) issatisfied or not: (a₄) each of the respective RMS values of thelower-order rotationally symmetric element, lower-order odd-symmetricelement, and lower-order even-symmetric element is 0.02λ or less; (b₄)each of the respective RMS values of the middle-order rotationallysymmetric element, middle-order odd-symmetric element, and middle-ordereven-symmetric element is 0.008λ or less; and (c₄) the RMS value of thehigher-order residual is 0.004λ or less.
 12. An evaluating methodaccording to claim 10, wherein said evaluating step evaluates whetherall of said conditions (a₃), (b₃), and (c₃) are satisfied or not.
 13. Anevaluating method according to claim 11, wherein said evaluating stepevaluates whether all of said conditions (a₄), (b₄), and (c₄) aresatisfied or not.
 14. An optical member for photolithography used in aspecific wavelength band at a wavelength of 250 nm or shorter; wherein,while a wavefront aberration measured upon transmitting light having awavelength λ through said optical member is expanded into a polynomialof a Zernike cylindrical function system, a rotationally symmetricelement, an odd-symmetric element, and an even-symmetric element in aterm where n=4 to 8 are defined as a lower-order rotationally symmetricelement, a lower-order odd-symmetric element, and a lower-ordereven-symmetric element, respectively; a rotationally symmetric element,an odd-symmetric element, and an even-symmetric element in a term wheren=9 to 35 are defined as a middle-order rotationally symmetric element,a middle-order odd-symmetric element, and a middle-order even-symmetricelement, respectively; and a rotationally symmetric element, anodd-symmetric element, and an even-symmetric element in a term wheren=35 to 80 are defined as a higher-order rotationally symmetric element,a higher-order odd-symmetric element, and a higher-order even-symmetricelement, respectively; and a term where n>80 is defined as a residual;said optical member satisfying at least one of the following conditions(a₁), (b₁), (c₁) and (d₁): (a₁) each of the respective RMS values of thelower-order rotationally symmetric element, lower-order odd-symmetricelement, and lower-order even-symmetric element is 0.06λ or less; (b₁)each of the respective RMS values of the middle-order rotationallysymmetric element, middle-order odd-symmetric element, and middle-ordereven-symmetric element is 0.02λ or less; (c₁) each of the respective RMSvalues of the higher-order rotationally symmetric element, higher-orderodd-symmetric element, and higher-order even-symmetric element is 0.005λor less; and (d₁) the RMS value of the residual is 0.006λ or less. 15.An optical member according to claim 14, wherein said optical membersatisfies at least one of the following conditions (a₂), (b₂), (c₂), and(d₂): (a₂) each of the respective RMS values of the lower-orderrotationally symmetric element, lower-order odd-symmetric element, andlower-order even-symmetric element is 0.02λ or less; (b₂) each of therespective RMS values of the middle-order rotationally symmetricelement, middle-order odd-symmetric element, and middle-ordereven-symmetric element is 0.008λ or less; (c₂) each of the respectiveRMS values of the higher-order rotationally symmetric element,higher-order odd-symmetric element, and higher-order even-symmetricelement is 0.003λ or less; and (d₂) the RMS value of the residual is0.004λ or less.
 16. An optical member according to claim 14, whereinsaid optical member satisfies all of said conditions (a₁) (b₁), (c1),and (d₁).
 17. An optical member according to claim 15, wherein saidoptical member satisfies all of said conditions (a₂) (b₂), (c₂), and(d₂).
 18. An optical member for photolithography used in a specificwavelength band at a wavelength of 250 nm or shorter; wherein, while awavefront aberration measured upon transmitting light having awavelength λ through said optical member is expanded into a polynomialof a Zernike cylindrical function system, a rotationally symmetricelement, an odd-symmetric element, and an even-symmetric element in aterm where n=4 to 8 are defined as a lower-order rotationally symmetricelement, a lower-order odd-symmetric element, and a lower-ordereven-symmetric element, respectively; a rotationally symmetric element,an odd-symmetric element, and an even-symmetric element in a term wheren=9 to 35 are defined as a middle-order rotationally symmetric element,a middle-order odd-symmetric element, and a middle-order even-symmetricelement, respectively; and a term where n>35 is defined as ahigher-order residual; said optical member satisfying at least one ofthe following conditions (a₃), (b₃), and (c₃): (a₃) each of therespective RMS values of the lower-order rotationally symmetric element,lower-order odd-symmetric element, and lower-order even-symmetricelement is 0.06λ or less; (b₃) each of the respective RMS values of themiddle-order rotationally symmetric element, middle-order odd-symmetricelement, and middle-order even-symmetric element is 0.02λ or less; and(c₃) the RMS value of the higher-order residual is 00.1λ or less.
 19. Anoptical member according to claim 18, wherein said optical membersatisfies at least one of the following conditions (a4), (b₄), and (c₄):(a₄) each of the respective RMS values of the lower-order rotationallysymmetric element, lower-order odd-symmetric element, and lower-ordereven-symmetric element is 0.02λ or less; (b₄) each of the respective RMSvalues of the middle-order rotationally symmetric element, middle-orderodd-symmetric element, and middle-order even-symmetric element is 0.008λor less; and (c₄) the RMS value of the higher-order residual is 0.004λor less.
 20. An optical member according to claim 18, wherein saidoptical member satisfies all of said conditions (a₃) (b₃), and (c₃). 21.An optical member according to claim 19, wherein said optical membersatisfies all of said conditions (a₄) (b₄), and (c₄).
 22. A projectionoptical system employed in a photolithography exposure apparatus used ina specific wavelength band at a wavelength of 250 nm or shorter, whereinat least 90% of lenses constituting said projection optical systemcomprise the optical member according to one of claims 14 to
 21. 23. Aprojection optical system according to claim 22, wherein, in saidlenses, a lens whose luminous flux diameter/effective diameter is ½ orless comprises the optical member according to claim
 17. 24. Aprojection optical system according to claim 22, wherein, in saidlenses, a lens whose luminous flux diameter/effective diameter is ½ orless comprises the optical member according to claim
 21. 25. Aphotolithography exposure apparatus used in a specific wavelength bandat a wavelength of 250 nmor shorter, said exposure apparatus comprisingthe projection optical system according to claim 22.